Adaptive critic apparatus and methods

ABSTRACT

A control apparatus and methods using context-dependent difference learning for controlling e.g., a plant. In one embodiment, the apparatus includes an actor module and a critic module. The actor module provides a control signal for the plant. The actor module is subject to adaptation, which is performed to optimize control strategy of the actor. The adaptation is based upon the reinforcement signal provided by the critic module. The reinforcement signal is calculated based on the comparison of a present control performance signal observed for a certain context signal, with a control performance signal observed for the same context in the past.

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BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to intelligent control systems and more particularly in one exemplary aspect to computer apparatus and methods for implementing an adaptive critic within e.g., an adaptive critic framework.

2. Description of Related Art

So-called “intelligent control” is a class of control techniques that utilize various computing approaches from artificial intelligence, including neural networks, Bayesian probability, fuzzy logic, machine learning, evolutionary computation and genetic algorithms (see White, D. and Sofge, D. (Eds.) (1992) Handbook of Intelligent Control: Neural, Fuzzy and Adaptive Approaches. Van Nostrand Reinhold, N.Y., incorporated herein by reference in its entirety). Intelligent controllers are finding increasing use today in complex systems control applications, such as for example autonomous robotic apparatus for navigation, perception, reaching, grasping, object manipulation, etc. (see Samad T., (Ed.) (2001) Perspectives in Control: New Concepts and Applications,” IEEE Press, N.J., incorporated herein by reference in its entirety).

Typically, intelligent controllers need to infer a relationship between the control signals (generated by the controller) and operational consequences upon a controlled apparatus (also referred to as “the plant”), that are described by changes of the plant state. Various learning methods are often used by intelligent controllers in order to approximate such relationships (see White and Sofge discussed supra; and Samad, T. (Ed.) (2001) Perspectives in Control Engineering. New York, each incorporated herein by reference in its entirety). By way of example, controllers that are used in tracking applications (such as, for example, robotic arms welding or painting car pieces along a predefined trajectory, mobile robots following predefined paths, etc.), aim to ensure that the plant state follows a desired trajectory (the target state trajectory) as closely as possible. In order to achieve trajectory tracking, the controller modifies control parameters (such as e.g. control gains) aiming to minimize an error between the target plant state (such as, for example, a desired robot configuration) and the actual (observed) plant state (such as, for example, an actual robot configuration) at every time instance. Performance of such controllers is typically quantified either by the magnitude of the tracking error, or by certain monotonic functions of the tracking error that are minimized, corresponding to minimized error between the target and actual state. Such functions are commonly referred to as the performance measures (see Goodwin G. (2001). Control System Design. Prentice Hall, incorporated herein by reference in its entirety).

Adaptive critic design (ACD) is a class of adaptive algorithms for intelligent control applications that is suitable for learning in noisy, nonlinear, and non-stationary dynamic systems. A family of ACD algorithms was proposed by Werbos P. J. (1992) in “Approximate dynamic programming for real-time control and neural modeling”. Handbook of Intelligent Control: Neural, Fuzzy and Adaptive Approaches, White D. A. and Sofge D. A. discussed supra, incorporated herein by reference in its entirety, as an optimization technique.

The ACD methods utilize two parametric blocks, commonly referred to as the controller (or the “actor”) and the “critic”, as described below with respect to FIG. 1. The actor implements various parameterized control rules and generates control signal. In a typical setup, the critic estimates a function that captures the effect that the control law will have on the control performance over multiple time periods into the future. Depending on this estimate, the critic sends a reinforcement signal to the actor. The actor uses the reinforcement signal to modify its control parameters in order to improve the control rules so as to minimize the performance measure, which is equivalent to minimizing the control errors. More details on various adaptive critic designs can be found in: Werbos P. J. (1992), or Prokhorov D. V and Wunsch D. C. (1997) Adaptive Critic Designs, IEEE Trans Neural Networks, vol. 8, No. 5, pp. 997-1007, each incorporated herein by reference in its entirety.

Referring now to FIG. 1, one typical implementation of the intelligent control apparatus according to prior art is described. The control apparatus 100 comprises a control block comprised of a critic module 108 and an actor block 104, configured to control operation of a plant 106, such as for example a robotic apparatus, a heating ventilation and cooling (HVAC) plant, autonomous vehicle, etc.

The control apparatus 100 is configured to perform control tasks in order to achieve the desired (target) plant state. The control apparatus 100 receives the input desired state signal x^(d)(t) (such as for example, a reference position of a robot, or a desired temperature for the heating ventilation and air conditioning (HVAC) system), and it produces a current plant state signal x(t). The control apparatus may further comprise a sensing or state estimation apparatus (not shown) that is used to provide a real-time estimate of the actual plant state x(t). The state signal x(t) typically represents full or partial dynamical state of the plant (e.g. current draw, motor position, speed, acceleration, temperature, etc.). In one variant, such as applicable to control applications where the full plant state x(t) is not available directly, various estimation methods may be used for state estimation, such as those described by Lendek Z. S., Babuska R., and De Schutter B. (2006) State Estimation under Uncertainty: A Survey. Technical report 06-004, Delft Center for Systems and Control Delft University of Technology, incorporated herein by reference in its entirety.

The control blocks 104, 108 of the control apparatus 100 receive the target state input x^(d)(t) via the pathways 102 and implement various parameterized control rules in order to generate the control signal u(t) (comprising for example, vehicle speed/direction in a position tracking application; or heater power/fan speed in an HVAC application). The control signal is provided to the plant 106 via the pathway 110, and is configured to move the current plant state x(t) towards the desired state (the target state) x^(d)(t). The control system 100 implements feedback control (closed-loop control), where the feedback signal x(t) is provided via the signaling lines 112 to the actor block. Alternatively, the control system 100 implements an open-loop control (feed-forward control) and in this case no feedback signal from the plant state to the actor is present. Other implementations exist, such as a combination of open-loop and close-loop control schemes.

The critic block 108 receives the target state input x^(d)(t) via the pathway 102, the control signal u(t) via the pathway 110, the current state signal x(t) via the pathway 112_1. The critic block 108 is configured to estimate the control performance function V(t), also referred to as the “cost-to-go”, that is typically defined for discrete systems as follows: V(t)=Σ_(k=0) ^(N)γ^(k) J(t+k),  Eqn. 1 where:

γ is a discount factor for finite horizon problems (0<γ<1);

k is the time step index; and

J(t) is the performance measure (also known as a utility function or a local cost) at time t.

For continuous systems, the summation operation in Eqn. 1 is replaced by an integral, and the term γ^(k) is replaced with an exponential function.

The ‘cost-to-go’ function V(t) captures the effect that the control rules (implemented by the actor block 104) have on the control performance of the control apparatus 100 over a predetermined period of time into the future.

At every time step k, the critic block 108 provides ‘guidance’ to the actor block 104 via the reinforcement signal R(t) via the pathway 114. For discrete time systems, the reinforcement signal R(t) is typically defined based on the current estimate of the cost function V(t) and a prior estimate of the cost function V(t−1) as follows: R(t)=J(t)+γV(t)−V(t−1)  (Eqn. 2)

where γ is the same constant parameter as in Eqn. 1. More details on this methodology are be found e.g. in R. S. Sutton and A. G. Barto (1998), Reinforcement Learning—An Introduction. MIT Press, incorporated herein by reference in its entirety.

For continuous time systems the reinforcement signal is calculated as: R(t)=J(t)−βV(t)+{dot over (V)}(t)  (Eqn. 3) where □ is a constant parameter and {dot over (V)}(t) is a time derivative of V(t). More details on the continuous time version are provided in; Kenji Doya (2000), Reinforcement Learning in Continuous Time and Space, Neural Computation, 12:1, 219-245, incorporated herein by reference in its entirety.

Typically, the actor block 104 has no a priori knowledge of the plant 106 dynamic model. Based on the reinforcement signal R(t), the actor block 104 modifies its control parameters (such as for example, gain) in order to generate the control signal u(t) which minimizes the cost-to-go function. For example, in the case of trajectory tracking or set-point control tasks, the minimization of the cost-to-go function corresponds to minimizing the cumulative error between the target and actual plant state, computed as the plant progresses along control trajectory towards the target state.

FIG. 2 illustrates a typical implementation of the critic module 108 for discrete systems in the considered class of control systems (i.e., for set-point control or trajectory tracking tasks) according to the prior art. As shown in FIG. 2, the critic apparatus 108 (denoted by a dashed rectangle) comprises the performance measure block 230, the value estimator block 220, the adjustment block 224, and the delay block 226. The performance measure block 230 calculates the performance measure J(t) given the desired plant state x^(d)(t) provided through pathway 202_1 and the actual plant state x(t) provided through pathway 212_1.

The value estimator block 220 in FIG. 2 receives the desired plant state signal x^(d)(t) provided through pathway 202, the actual plant state signal x(t) provided through pathway 212, the control signal u(t) provided through the pathway 210, and reinforcement signal R(t) provided through the pathway 214. At each discrete step of the critic block operation, the value estimator block 220 generates a cost-to-go value signal V(t), based on the received inputs. The reinforcement signal R(t) is used by the value estimator block 220 to modify internal value estimator parameters as described in, e.g., Werbos; White D. A. and Sofge D. A.; or Prokhorov D. V and Wunsch D. C., discussed supra.

The adjustment block 224 (denoted by the γ symbol in FIG. 2 receives the value signal V(t) through the pathway 232 and produces the discounted value signal γV(t). The delay block 226 (denoted by symbol z⁻¹ in FIG. 2) receives the value signal V(t) through the pathway 232_1 and produces the value signal delayed by one simulation step, which is denoted as V(t−1) in FIG. 2. The reinforcement signal R(t) is then calculated by the computation block 240 as defined by Eqn. 2., given the performance signal J(t) provided through the pathway 218, the discounted value γV(t) produced by the adjustment block 224 and the delayed value signal V(t−1) provided by the delay block 226.

FIG. 2A illustrates a typical implementation of the critic block for continuous time control systems according to the prior art. As shown in FIG. 2A, the critic apparatus 208 (depicted by a dashed rectangle) comprises the value block 220, the performance measure block 230, the β-block 244 and the derivative block 248 (denoted in the FIG. 2A as d/dt). The value block 220 and the performance measure block 230 receive and produce the same signals and operate similarly to the discrete-time control apparatus described with respect to FIG. 2, supra. The β-block 244 of FIG. 2A receives the value signal V(t) through the pathway 232 and produces the discounted value signal βV(t). The derivative block 248 receives the value signal V(t) through the pathway 232_1, and produces the temporal derivative of the value signal {dot over (V)}(t). The reinforcement signal R(t) is calculated by the computation block 250 according to the relationship defined in Eqn. 3, given the performance signal J(t) provided through the pathway 218, the discounted value βV(t) produced by the β-block 244 and the temporal derivative {dot over (V)}(t) of the value signal provided by the derivative block 248.

Traditional ACD approaches, such as those described with respect to FIGS. 2 and 2A, suffer from several shortcomings, such as for example requiring estimates of future performance of the control system. Such predictions invariably are of limited accuracy, and often suffer from the problem of the “curse of dimensionality”; i.e., when system control solutions become unattainable as the number of the variables governing the dynamic system model increases.

Accordingly, there is a salient need for an adaptive critic design apparatus and associated methods that aim at optimizing control rules without the foregoing limitations; e.g., that are based on the observed present and past control system performance.

SUMMARY OF THE INVENTION

The present invention satisfies the foregoing needs by providing, inter alia, apparatus and methods for intelligent control, including apparatus and methods for implementing critic designs using adaptive learning.

In first aspect of the invention, a computerized control apparatus configured to optimize control of an apparatus e.g., robotic device) is described. In one embodiment, the control apparatus comprises a plant block in communication with the robotic device, the plant block configured to output a current plant state signal, an actor block configured to receive a target plant state signal, a current plant state signal, and a reinforcement signal, and to communicate a control signal to the plant block, and a critic block configured to receive the control signal from the actor block, and to provide the reinforcement signal to the actor block. In one variant, the critic block comprises an interpolator configured to receive the target plant state signal, a present value of the current plant state signal, and a present performance value, and to provide a prior performance value; and a comparator configured to determine the reinforcement signal based at least in part on the past performance value and the present performance value. The present value of the current plant state signal corresponds to a second time instance and the present performance value configured based at least in part on the target plant state signal and the present value of the current plant state signal, and the prior performance value is selected by the interpolator based at least in part on (i) the present value of the current plant state signal being within a first predetermined threshold from a past value of the current plant state signal, the past value of the current plant state signal corresponding to a first time instance, and (ii) the target plant state signal being within a second predetermined threshold from a past value of the target plant state signal, the past value of the target plant state signal corresponding to the first time instance; and

In second aspect of the invention, a computerized adaptive critic apparatus is described. In one embodiment, the critic apparatus comprises first logic configured to receive a reference signal and a plant state signal, and second logic configured to provide a reinforcement indication being determined based at least in part on (i) a present value of the plant state signal corresponding to a first time instance, and (ii) a present value of the reference signal corresponding to the first time instance.

In one variant, the reinforcement indication is determined based at least in part on a past performance value corresponding to a second time instance, and a present performance value corresponding to the first time instance, the second time instance preceding the first time instance.

In another variant, the critic apparatus comprises an interpolator block configured to receive the reference signal, the plant state signal, and a first performance value, and to provide a second performance value, the first performance value is associated with the first time instance; and the second performance value is based at least in part on a past control performance, associated with a second time instance, the second time instance preceding the first time instance.

In another variant, the first and second logic comprise a computer readable storage medium having at least one computer program stored thereon, the at least one program being configured to, when executed on a processing device: receive a reference signal and a plant state signal, and provide the reinforcement indication.

In yet another variant, the first and second logic are comprised, at least in part, of gate logic of an integrated circuit.

In a third aspect of the invention, an adaptive apparatus is disclosed. In one embodiment, the adaptive apparatus is adapted for use in a computerized controller, the computerized controller configured to optimize control of a functional apparatus, and the adaptive apparatus comprises: first logic configured to receive at a first time a context value, second logic configured to determine a value of a performance signal of the computerized controller corresponding to the first time, the determination based at least in part on the context value, and third logic configured to provide a reinforcement indication adapted to cause modification of at least one control parameter of the computerized controller, the modification configured to minimize an error value associated with the performance signal, the reinforcement indication is determined based at least in part on the value of the performance signal.

In one variant, the context value comprises a context vector, the reinforcement indication is further determined based at least in part on a past value of the performance signal, the past value associated with a second time preceding the first time, and the past value of the performance signal is determined based at least in part on a match between the context vector and a past context vector corresponding to the second time, the past value of the performance signal is determined based at least in part on a value of the performance signal determined at the second time based on the past context vector.

In another variant, the adaptive apparatus comprises a plant block in communication with the functional apparatus, the plant block configured to provide a plant state to the adaptive apparatus, and an actor block in communication with the plant block and the adaptive apparatus the actor block configured to receive the reinforcement indication, configured to cause modification of at least one control parameter associated with control of the functional apparatus so as to effect optimized control of the functional apparatus. The context value comprises a first value of a reference signal, corresponding to the first time and a first value of the plant state corresponding to the first time, and the past context vector comprises a second value of the reference signal, corresponding to a second time and a second value of the plant state, corresponding to the second time.

In yet another variant, the past value of the performance signal is configured based at least in part on (i) the first value of the plant state being within a first predetermined threshold from the second value of the plant, (ii) the first value of the reference signal being within a second predetermined threshold from the second value of the reference signal, (iii) the value of the performance signal, and (iv) a past value of the performance signal determined at the second time based at least in part on the second value of the reference signal and the second value of the plant state.

In a fourth aspect of the invention, method for computerized intelligent control is disclosed. In one embodiment, the method comprises receiving a first context indicator associated with a first time, determining a first performance value based at least in part on the first context indicator, and providing a reinforcement indication, the reinforcement indication being determined based at least in part on the first performance value, the reinforcement indication further configured to enable modification of at least one control parameter associated with control of a functional apparatus.

In one variant, the modification is configured to reduce at least one error measure associated with control of the functional apparatus, relative to control of the functional apparatus in absence of the reinforcement indication, and the first context indicator comprises a reference state signal and a current state signal, the current state associated with control of the functional apparatus.

In another variant, the reinforcement indication is being determined based at least in part on a past performance value provided by an interpolator block, and the first performance value comprises a teaching signal configured to effect supervised learning of the interpolator block, the teaching signal being determined based at least in part on a parameterized function of at least one of the reference signal the current state signal. The parameterized function is characterized by at least one parameter, and the supervised learning is configured to modify the at least one parameter.

In another variant, the supervised learning comprises online learning effected during operation of the functional apparatus, the function is configured to compute a running mean of a plurality of performance values corresponding to a plurality of time instances and the at least one parameter comprises a number of performance values of the plurality of the performance values used in computing the running mean, and each time instance of the plurality of time instances preceding the first time.

In another aspect of the invention, an adaptive critic-controlled system is disclosed. In one embodiment, the system comprises an adaptive critic apparatus such as that referenced supra, and a controlled apparatus (such as e.g., a robotic device).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of typical control system architecture within the adaptive critic design framework according to the prior art.

FIG. 2 is a block diagram illustrating one implementation of an adaptive critic of the control apparatus of FIG. 1 for discrete-time control systems according to the prior art.

FIG. 2A is a block diagram illustrating one implementation of an adaptive critic of the control apparatus of FIG. 1 for the continuous-time systems according to the prior art.

FIG. 3 is a block diagram illustrating one embodiment of an adaptive critic apparatus according to the invention.

FIG. 4 is a plot illustrating one embodiment of interpolator block operation of the adaptive critic apparatus of FIG. 3 according to the invention.

FIG. 5 is a logical flow chart illustrating one embodiment of the method of adaptive critic operation according to the invention.

FIG. 5A is a logical flow chart illustrating one embodiment of the method of control apparatus operation according to the invention.

All Figures disclosed herein are © Copyright 2011 Brain Corporation. All rights reserved.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Exemplary embodiments of the present invention will now be described in detail with reference to the drawings, which are provided as illustrative examples so as to enable those skilled in the art to practice the invention. Notably, the figures and examples provided herein are not meant to limit the scope of the present invention to a single embodiment, but other embodiments are possible by way of interchange of or combination with some or all of the described or illustrated elements. Wherever convenient, the same reference numbers will be used throughout the drawings to refer to same or like parts.

Where certain elements of these embodiments can be partially or fully implemented using known components, only those portions of such known components that are necessary for an understanding of the present invention will be described, and detailed descriptions of other portions of such known components will be omitted so as not to obscure the invention.

In the present specification, an embodiment showing a singular component should not be considered limiting; rather, the invention is intended to encompass other embodiments including a plurality of the same component, and vice-versa, unless explicitly stated otherwise herein.

Further, the present invention encompasses present and future known equivalents to the components referred to herein by way of illustration.

As used herein, the terms “computer”, “computing device”, and “computerized device”, include, but are not limited to, personal computers (PCs) and minicomputers, whether desktop, laptop, or otherwise, mainframe computers, workstations, servers, personal digital assistants (PDAs), handheld computers, embedded computers, programmable logic device, personal communicators, tablet computers, portable navigation aids, J2ME equipped devices, cellular telephones, smart phones, personal integrated communication or entertainment devices, or literally any other device capable of executing a set of instructions and processing an incoming data signal.

As used herein, the term “computer program” or “software” is meant to include any sequence or human or machine cognizable steps which perform a function. Such program may be rendered in virtually any programming language or environment including, for example, C/C++, C#, Fortran, COBOL, MATLAB™, PASCAL, Python, assembly language, markup languages (e.g., HTML, SGML, XML, VoXML), and the like, as well as object-oriented environments such as the Common Object Request Broker Architecture (CORBA), Java™ (including J2ME, Java Beans, etc.), Binary Runtime Environment (e.g., BREW), and the like.

As used herein, the term “memory” includes any type of integrated circuit or other storage device adapted for storing digital data including, without limitation, ROM, PROM, EEPROM, DRAM, SDRAM, DDR/2 SDRAM, EDO/FPMS, RLDRAM, SRAM, “flash” memory (e.g., NAND/NOR), and PSRAM.

As used herein, the terms “integrated circuit”, “chip”, and “IC” are meant to refer to an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material and generally include, without limitation, field programmable gate arrays (e.g., FPGAs), a programmable logic device (PLD), reconfigurable computer fabrics (RCFs), application-specific integrated circuits (ASICs).

As used herein, the terms “microprocessor” and “digital processor” are meant generally to include all types of digital processing devices including, without limitation, digital signal processors (DSPs), reduced instruction set computers (RISC), general-purpose (CISC) processors, microprocessors, field programmable gate arrays (e.g., FPGAs), PLDs, reconfigurable computer fabrics (RCFs), array processors, secure microprocessors, and application-specific integrated circuits (ASICs). Such digital processors may be contained on a single unitary IC die, or distributed across multiple components.

As used herein, the terms “state” and “plant state” refer, without limitation, to a set of variables used to describe the full or partial dynamic state of the plant.

Overview

Apparatus and methods for the adaptive critic design directed at optimizing control rules that are based primarily on the observed present and past control system performance are disclosed. This approach advantageously improves control performance of the control apparatus of the invention, compared to the existing ACD solutions. The improvement is due to, in part, the use of the present performance measure, which is a directly observable quantity, and is used as the training target during the adaptive critic training phase.

In one embodiment, the critic apparatus of the invention advantageously generates a reinforcement signal based on the value of the present control performance quantified by the performance measure observed for the certain context, with an estimate of the past control performance value J for the same context. The input context may comprise a vector composed of the plant state and a target plant state trajectory (the desired plant state).

Thus, unlike in the traditional ACDs, the role of the critic of the present invention is to estimate past system performance rather than the future performance. This configuration advantageously facilitates training of the critic apparatus, as described above.

The present invention provides, in one salient aspect, apparatus and methods for implementing an adaptive-critic for intelligent control of a plant within the adaptive critic framework. The described methods aim at minimizing an instantaneous error between the desired plant state and the actual (observed) plant state. The methods and apparatus of the invention are useful for, but are not limited to, a category of trajectory tracking or set-point control tasks.

In a broader sense, the invention provides methods and apparatus for solving a problem of function approximation: given certain inputs to the system, the exemplary embodiments of the invention generate output signals that predict the target output signals.

Detailed Description of Exemplary Embodiments

Detailed descriptions of the various embodiments and variants of the apparatus and methods of the invention are now provided.

Embodiments of the invention may be for example deployed in a hardware and/or software implementation of a computer-controlled system, provided in one or more of a prosthetic device, robotic device and any other specialized apparatus. In one such implementation, an control system may include a processor embodied in an application specific integrated circuit (ASIC), a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP) or an application specific processor (ASIP) or other general purpose multiprocessor, which can be adapted or configured for use in an embedded application such as controlling a robotic device. However, it will be appreciated that the invention is in no way limited to the foregoing applications and/or implementations.

Exemplary Critic Apparatus

The present invention provides, in one salient aspect, apparatus and methods for implementing an adaptive-critic apparatus directed at minimizing an instantaneous error between the target state and actual (observed) plant state.

FIG. 3 illustrates one embodiment of the critic apparatus (for use in applications such as the critic module 108 of FIG. 1) according to the invention. While described primarily in the context of continuous and/or discrete control apparatus (such as the control apparatus 100 of FIG. 1), the apparatus 308 may be used in any number of other applications or host apparatus, the apparatus of FIG. 1 being merely exemplary.

As shown in FIG. 3, the adaptive critic apparatus 308 (depicted by a dashed rectangle) comprises an interpolator block 320, a performance estimation block 330, and a comparator block 340. The critic 308 is configured to receive the reference input signal x^(d)(t), corresponding to the desired (predicted or target) plant state, the actual plant state x(t) (or its estimate), and the control signal u(t) (such as for example, currents driving the robot motors, vehicle speed and direction, or heater power and fan speed, etc). Note, that the input signals x^(d)(t)={x^(d) _(i)(t), i=1:N}, x(t)={x_(i)(t), i=1:NN, NN<N}, u(t)={u_(i)(t),i=1:M} comprise multiple components and are typically described using vector quantities.

Although the critic apparatus 308 receives some inputs that are generally similar to the prior art critic apparatus 108 of the adaptive critic designs system of FIG. 1, the critic 308 is structurally different from the prior art (compare the exemplary configuration of FIG. 3 to FIG. 2 and FIG. 2A), and performs different functions as described in detail below.

As shown in FIG. 3, the target state x^(d)(t) and the output plant state signal x(t) are routed to performance estimation block 330 via the logical pathways 302_1, 312_1, respectively, and to the interpolator block 320 via the logical pathways 302, 312, respectively. In addition, the control signal u(t) is routed to the interpolator block 320 via the logical pathway 310.

The control performance of the control apparatus (e.g., the apparatus 100 of FIG. 1) is typically expressed using a performance measure J(t), which describes an error estimate between the target state x^(d)(t) and the current plant state x(t) at every time instance. Without loss of generality, it is assumed that the measure J(t) is defined such that the control performance improvement is equivalent to the minimization of J(t) with respect to time. It is also assumed that the current plant state x(t) (or its estimates) are available to the performance measure block 320 at every time instance of the adaptive critic 308 operation.

As shown in FIG. 3, the current estimate of the performance measure J(t) is delivered to the interpolator via the pathway 322.

In one variant, the target state signal x^(d)(t), the current state signal x(t) and the control signal u(t), together form a context signal c(t) and the performance signal J(t) is expressed as a function of the context signal, as follows: J(t)=J(c(t)),c(t)=[x ^(d)(t)x(t)u(t)]^(T)  (Eqn. 4)

As discussed in further detail below, the interpolator block 320, in accordance with the received context signal c(t), and the current control performance signal J(c(t)), stores information about the present value of J(c(t)), and provides a prior performance estimate J_(o)(c(t)) to the comparator block 340 via the pathway 324, as shown in FIG. 3. The prior performance measure value J_(o)(c(t)), stored by the interpolator block 320, corresponds to the control performance value observed (computed) by the performance measurement block 330 for the same context c(t) as the current performance J(c(t)), but at certain time instances preceding the current time instance t.

The comparator 340 receives the present performance value J(c(t)) and an estimate of the past performance value J_(o)(c(t)), and produces the signal R(t) (also referred to as the reinforcement signal), which is a measure of the distance between both input signals. That is: R(t)=(J(c(t)),J _(o)(c(t))).  (Eqn. 6) In one variant, the signal R(t) is defined as a weighted difference between J(c(t)) and J_(o)(c(t)), that is: R(t)=αJ(c(t))−βJ _(o)(c(t)),  (Eqn. 7) where α, β are constants, selected in one variant such that 0≦α<1, 0≦β<1. Interpolator Apparatus

The critic apparatus 308 of the embodiment shown in FIG. 3 advantageously comprises the interpolator block 320, which is configured to, inter alia, store the information related to the past performance of the control apparatus (e.g., the apparatus 100 of FIG. 1). Specifically, the interpolator block 320 stores the past values J_(o)(t) of the performance measure J for every instance of the context signal c(t). In one variant, the interpolator block 320 is further configured to generalize the acquired knowledge (i.e., the relationship between of the past performance and the context) and to interpolate and/or extrapolate to other context signal instances never seen during the learning phase. One exemplary embodiment of such interpolation is illustrated in FIG. 4.

As shown in FIG. 4, line 402 depicts a control trajectory 402 relating the past performance J_(o)(t) and the context c(t). Circles labeled 404_1, 404_2 represent instances of past performance J1, J2 computed (and stored by the interpolator) for specific instances of context c₁ and c₂. The circle 406 labeled with an “x” corresponds to the context configuration c_(x) that was not previously observed. Hence, the interpolator does not have the corresponding performance measure Jx stored in its storage block. However, upon receiving the context configuration c_(x) the interpolator determines that the new context c_(x) is within the range of previously observed contexts (i.e., the range [c₁, c₂]). Subsequently, the interpolator determines (interpolates) the past performance measure Jx_(o) that corresponds to the context c_(x), even though the context c_(x) was not previously observed by the interpolator of the adaptive critic apparatus 308.

In a more general sense, the interpolator block 320 implements the following mapping: c(t)→J _(o)(c(t))  (Eqn. 8)

In one variant, of context of trajectory tracking tasks, at every time instance t_(n) the mapping associates the present instance of the context vector c(t_(n)) (comprising, for example, the instantaneous target state value x^(d) and the current plant state value x taken at the present time t_(n)) with an average tracking error <J(c(t_(k)))>, where the average is calculated over the past instances of the tracking error J(c(t_(k))) at time instances t_(k), k=1:K, where t_(k) are selected such that at t_(k):c(t_(k))=c(t_(n)), k=1:K. In other words, the past system performance J_(o)(c(t)) in Eqn. 8. is calculated as the average <J(c(t_(k)))>, where the average is computed over the past values of J(c(t_(k)))) when the present instance of the vector c has been previously observed.

It is appreciated by those skilled in the arts that other statistical functions (e.g., a running mean, a weighted average, a median, etc.) may be used in place of the averaging when computing the mapping of Eqn. 8. It is further appreciated by a skilled practitioner of the arts that averaging time scales (i.e., the number of elements of a running mean) and/or the weighting parameters are determined based on a specific application using any of applicable techniques, such as, for example, least squares fit, minimum mean squared error, median absolute deviation, etc.

In another variant, the past performance measure is computed using an iterative approach. In such implementation, the actual system performance observed in the present trial n is denoted by J(t)^(n). The expected system performance in the n^(th) trial, denoted by J_(o)(t)^(n), is defined an average system performance over the last k trials preceding n. Values of J_(o)(t)^(n) are computed using the following iterative procedure:

$\begin{matrix} {{{J_{o}(t)}^{n} = \frac{{J(t)}^{({n - 1})} + {{kJ}_{o}(t)}^{({n - 1})}}{k + 1}},{{{where}\mspace{14mu}{J_{o}(t)}^{1}} = {{J(t)}^{1}.}}} & \left( {{Eqn}.\mspace{11mu} 9} \right) \end{matrix}$

Several approaches are used to implement the mapping of Eqn. 8. In one variant of the invention, when the context consists of a finite number of states, the interpolator is implemented as a look-up table (or a similar method). In this variant, each cell i in the look-up table, corresponds to a different context c_(i), where i=1, 2, . . . is the common label of the context value and the cell. The table is initiated with some values J_(oi). For example, initially all cells in the table may take zero values. Whenever a given context c_(i) is visited the table outputs a value J_(oi) stored in the i^(th) cell corresponding to c_(i) and updates the cell based on the observed value of the present performance signal J(t). In one exemplary variant of the invention the cells are updated using the most present values of the performance measure signal J(t) according to the following rule: if c(t)=c _(i)(t) then J _(oi) =αJ _(oi) +βJ(t),  (Eqn. 9) where α,β are constants, selected in one variant such that 0≦α<1, 0≦β<1.

In another variant of the invention, when the context consists of an infinite number of states, the past performance J_(o)(c(t)) is estimated using function approximation methods, for example, using an artificial neural network model trained according to the online supervised learning algorithm, such as e.g. a delta rule or an error back-propagation algorithm as an approximation block (see e.g. Hertz et al., Introduction to the theory of neural computation. Westview Press, 1991) aiming at minimizing the difference between the present performance signal J(c(t)) and the approximation output J_(o)(c(t)) (see FIG. 3). Since online approximation methods have a limited convergence speed, the output from the interpolator will follow, but will never (except of, after infinite number of iterations) perfectly be equal to the present value of the performance measure J(c(t)), thus the output J_(o)(c(t)) from the approximation block will represent some history (e.g. a running average) of the past values of J(c(t)), as desired.

Exemplary Critic Method

FIG. 5 illustrates one exemplary method of the adaptive critic operation according to the invention. At step 502, the critic receives the present context value (e.g., the context vector c(t) defined by Eqn. 4) corresponding to the present time t0. Subsequently, at step 504, the critic determines the present value of the performance signal J(t) that corresponds to the present context value c(t)). At step 506, the present performance J(t) and the present context c(t) are provided to the interpolator, which compares at step 508 the present context value c(t) to the context values <c> that were observed previously to time t0 (the observed context space). Based on the evaluation of the observed context space, the interpolator determines at step 510 the value of the past performance Jo(t) that corresponds to the present value of the context c(t) using any of the methodologies described, supra. At step 512 the comparator determines the reinforcement signal R(t) based on the present performance value J(t) and the past performance value Jo(t), and provides the reinforcement signal to the actor block at step 514.

Referring now to FIG. 5A, one exemplary method of the control apparatus operation according to the invention is shown and described. At step 532 the actor block (such as for example the actor 104 of FIG. 1) receives the reinforcement signal R(t) from the comparator (such as for example, the comparator block 340 of FIG. 3) At step 534, the actor uses the reinforcement signal R(t) to modify parameters of the actor module, according to the actor learning policy, thereby generating the new control signal u⁺(t), such that to minimizing the performance measure in subsequent iterations of the control apparatus operation.

Exemplary Uses and Applications of Certain Aspects of the Invention

Adaptive critic apparatus and methods of the invention advantageously allow for an improved intelligent controller operation due to, inter alia, the use of past values of controller performance that are previously observed for the present values of the controller input (i.e., the context). The use of past (observed) performance in place of the future (i.e., predicted) performance is advantageous as it reduces (or altogether eliminates) controller susceptibility to possible model and prediction errors.

In one embodiment, the adaptive critic is implemented as a software library configured to be executed by a in intelligent control apparatus running various control applications. In another embodiment, the adaptive critic comprises a specialized hardware module (e.g., an embedded processor or controller). In another embodiment the adaptive critic apparatus is implemented in a specialized or general purpose integrated circuit, such as, for example ASIC, FPGA, or PLD). Myriad other implementations exist that will be recognized by those of ordinary skill given the present disclosure.

Advantageously, the present invention can be used to simplify and improve control tasks related to trajectory tracking or set-point control in such tasks as painting or welding using robotic devices, stabilization of inherently unstable control objects, such as a Segway®, etc. Embodiments of the present invention are further applicable to a wide assortment of control applications including industrial control, navigation of autonomous vehicles, robotics. Advantageously, exemplary embodiments of the present invention are useful in a variety of devices including without limitation prosthetic devices (such as artificial limbs), industrial control, autonomous and robotic apparatus, HVAC, and other electromechanical devices requiring accurate stabilization, set-point control or trajectory tracking functionality. Examples of such robotic devises are manufacturing robots (e.g., automotive), military devices, and medical devices (e.g. for surgical robots). Examples of autonomous vehicles include rovers, unmanned air vehicles, underwater vehicles, smart appliances (e.g. ROOMBA®), etc. Various other applications exist that will be recognized by those of ordinary skill given the present disclosure.

It will be recognized that while certain aspects of the invention are described in terms of a specific sequence of steps of a method, these descriptions are only illustrative of the broader methods of the invention, and may be modified as required by the particular application. Certain steps may be rendered unnecessary or optional under certain circumstances. Additionally, certain steps or functionality may be added to the disclosed embodiments, or the order of performance of two or more steps permuted. All such variations are considered to be encompassed within the invention disclosed and claimed herein.

While the above detailed description has shown, described, and pointed out novel features of the invention as applied to various embodiments, it will be understood that various omissions, substitutions, and changes in the form and details of the device or process illustrated may be made by those skilled in the art without departing from the invention. The foregoing description is of the best mode presently contemplated of carrying out the invention. This description is in no way meant to be limiting, but rather should be taken as illustrative of the general principles of the invention. The scope of the invention should be determined with reference to the claims. 

What is claimed:
 1. An adaptive apparatus for use in a computerized controller, the computerized controller configured to optimize control of a functional apparatus, the adaptive apparatus comprising: a first logic configured to receive at a first time a context value comprising a context vector; a second logic configured to determine a value of a performance signal of the computerized controller that corresponds to the first time, the determination based at least in part on the context value; and a third logic configured to provide a reinforcement indication adapted to cause a modification of at least one control parameter of the computerized controller, the modification configured to minimize an error value associated with the performance signal; wherein: the adaptive apparatus is further configured to receive a plant state from a plant block in communication with the adaptive apparatus; the adaptive apparatus is further configured to provide the reinforcement indication to an actor block in communication with the adaptive apparatus, the reception of the reinforcement indication configured to cause a modification of at least one control parameter associated with control of the functional apparatus so as to effect optimized control of the functional apparatus; the reinforcement indication is determined based at least in part on the value of the performance signal; the context value comprises a first value of a reference signal that corresponds to the first time, and a first value of the plant state that corresponds to the first time; a past context vector comprises a second value of the reference signal that corresponds to a second time, and a second value of the plant state that corresponds to the second time; and a past value of the performance signal that is configured based at least in part on: (i) the first value of the plant state being within a first predetermined threshold from the second value of the plant state; (ii) the first value of the reference signal being within a second predetermined threshold from the second value of the reference signal; (iii) the value of the performance signal; and (iv) the past value of the performance signal determined at the second time based at least in part on the second value of the reference signal and the second value of the plant state.
 2. The adaptive apparatus of claim 1, wherein the past value of the performance signal is further configured based at least in part on a first value of a control signal, that corresponds to the first time, the first value of the control signal being within a third predetermined threshold from a second value of the control signal that corresponds to the second time; and the value of the performance signal is further determined based at least on the second value of the control signal that corresponds to the second time.
 3. The adaptive apparatus of claim 2, wherein the third logic comprises a comparator component configured to determine the reinforcement indication based on at least in part on the past value of the performance signal and the value of the performance signal.
 4. The adaptive apparatus of claim 3, wherein the reinforcement indication is determined as a weighted difference between the past value of the performance signal and the value of the performance signal.
 5. The adaptive apparatus of claim 1, wherein the third logic comprises an interpolator component configured to: receive the reference signal, the plant state, and the value of the performance signal; and provide the past value of the performance signal; wherein: the value of the performance signal is associated with the first time instance; and the past value of the performance signal is based at least in part on a past control performance, associated with a second time instance, where the second time instance precedes the first time instance.
 6. The adaptive apparatus of claim 5, wherein the past value performance value is further based at least in part on (i) a match between a set of values, the set of values comprising the second value of the reference signal that corresponds to the second time instance, and a second value of the plant state signal that corresponds to the second time instance; (ii) and a third value of the performance signal determined by the interpolator block at the second time instance for the set of values.
 7. The adaptive apparatus of claim 6, wherein the interpolator block is configured to map (i) the first value of the reference signal and the first value of the plant state signal, where both of the first value of the reference signal and the second value of the plant state signal correspond to the first time instance, with (ii) the past value of the performance signal, using supervised learning.
 8. The adaptive apparatus of claim 5, wherein: the past value of the performance signal is determined as a running mean of a plurality of performance values that correspond to a plurality of time instances, individual time instances of the plurality of time instances preceding the first time instance; and individual ones of the plurality of performance values being determined based at least in part on a value group comprising the reference signal that corresponds to a respective time interval of the plurality of time instances.
 9. The adaptive apparatus of claim 1, wherein the first and second logic comprise a computer readable storage medium having at least one computer program stored thereon, the at least one program being configured to, when executed on a processing device: perform the reception of the reference signal and the plant state signal; and provide the reinforcement indication.
 10. The adaptive apparatus of claim 1, wherein the first and second logic are comprised, at least in part, of a gate logic of an integrated circuit.
 11. The adaptive apparatus of claim 1, wherein the past value of the performance signal is determined based at least in part on a value of the performance signal determined at the second time based on the past context vector.
 12. The adaptive apparatus of claim 11, wherein the past value of the performance signal is determined based at least in part on a distance between the context vector and the past context vector being smaller than a predetermined measure.
 13. A method of operating a computerized adaptive controller apparatus, the controller apparatus configured to optimize control of a functional apparatus, the method comprising: receiving at a first time a context value comprising a context vector; determining a value of a performance signal of the computerized controller that corresponds to the first time, the determination based at least in part on the context value; determining, based at least in part on the value of the performance signal, a reinforcement indication adapted to cause a modification of at least one control parameter of the computerized controller, the modification configured to minimize an error value associated with the performance signal so as to effect optimized control of the functional apparatus; and obtaining a state information associated with the functional apparatus; wherein: the context vector comprises a first value of a reference signal that corresponds to the first time, and a first value of the state information that corresponds to the first time; a past context vector comprises a second value of the reference signal that corresponds to a second time, and a second value of the plant state that corresponds to the second time; the reinforcement indication is determined based at least in part on a past value of the performance signal, the past value associated with the second time preceding the first time; the past value of the performance signal is determined based at least in part on a match between the context vector and the past context vector corresponding to the second time; the past value of the performance signal is determined at the second time based at least in part on the second value of the reference signal and the second value of the plant state; and the value of the performance signal is configured based at least in part on: (i) the first value of the plant state being within a first predetermined threshold from the second value of the plant state; (ii) the first value of the reference signal being within a second predetermined threshold from the second value of the reference signal; and (iii) the value of the performance signal.
 14. The method of claim 13, wherein the minimization of the error value is configured to reduce at least one error measure associated with the control of the functional apparatus, relative to the control of the functional apparatus in absence of the reinforcement indication.
 15. The method of claim 14, wherein the reference signal comprises a reference plant state.
 16. The method of claim 15, wherein: the performance value comprises a teaching signal configured to effect supervised learning of the interpolator block, the teaching signal being determined based at least in part on a parameterized function of at least one of the reference plant state or the first value of the plant state, the parameterized function characterized by at least one parameter; and the supervised learning is configured to modify the at least one parameter.
 17. The method of claim 16, wherein: the parameterized function is configured to compute a running mean of a plurality of performance values corresponding to a plurality of time instances, and the at least one parameter comprises a number of performance values of the plurality of the performance values used in computing the running mean; and each time instance of the plurality of time instances precedes the first time.
 18. The method of claim 17, wherein the supervised learning comprises online learning effected during operation of the functional apparatus.
 19. An adaptive apparatus for use in a computerized controller, the computerized controller configured to optimize control of a functional apparatus, the adaptive apparatus comprising: means for receiving at a first time a context value comprising a context vector; means for determining a value of a performance signal of the computerized controller that corresponds to the first time, based at least in part on the context value; and means for providing a reinforcement indication adapted to cause a modification of at least one control parameter of the computerized controller, the modification configured to minimize an error value associated with the performance signal; means for providing a plant state to the adaptive apparatus; and means for receiving the reinforcement indication, the means for receiving the reinforcement indication configured to cause modification of at least one control parameter associated with control of the functional apparatus so as to effect optimized control of the functional apparatus; wherein: the reinforcement indication is determined based at least in part on the value of the performance signal; the context value comprises a first value of a reference signal that corresponds to the first time, and a first value of the plant state that corresponds to the first time; the past context vector comprises a second value of the reference signal that corresponds to a second time, and a second value of the plant state that corresponds to the second time; and a past value of the performance signal is configured based at least in part on: (i) the first value of the plant state being within a first predetermined threshold from the second value of the plant state; (ii) the first value of the reference signal being within a second predetermined threshold from the second value of the reference signal; (iii) the value of the performance signal; and (iv) the past value of the performance signal determined at the second time based at least in part on the second value of the reference signal and the second value of the plant state.
 20. The adaptive apparatus of claim 19, wherein: the past value of the performance signal is further configured based at least in part on a first value of a control signal, that corresponds to the first time, the first value of the control signal being within a third predetermined threshold from a second value of the control signal that corresponds to the second time; and the means for determining the value of the performance signal are further based at least on the second value of the control signal that corresponds to the second time. 